Some of the most interesting experimental phenomena occur at filling factors (ratio of the number of
electrons and the number of flux quanta) \(\nu = \tfrac{1}{2}\)  and \(\nu =\tfrac{5}{2}\) , even-denominator fractions. The gapless
system at \(\nu =\tfrac{1}{2}\)  is believed to be in a Fermi liquid state of underlying quasiparticles - composite fermions (CFs), as proposed and described in [1]} early on, while it is believed that incompressible (gapped) FQHE at \(\nu = \tfrac{5}{2}\)  can be
associated with some kind of \(p\) -wave pairing of CFs in the second LL (sLL), as
proposed in [2]}. To understand more closely these systems, one may start by focusing on
an isolated half-filled LL, the lowest LL (LLL) at \(\nu =\tfrac{1}{2}\)  in the case of the CF liquid (CFL), and sLL at \(\nu = \tfrac{5}{2}\)  in the case of the gapped system.
